Marbles come in two sizes: 1-inch diameter and 2-inch diameter. The 1-inch diameter marbles cost 30 cents less than the 2-inch marbles. Rochelle buys 25 1-inch marbles for her science project and spends exactly $10. Find the cost of a 2-inch marble.(1 point)

Question

Responses

$2.50
$2.50

$0.10
$0.10

$0.70
$0.70

$2.80

Answer 1

Let the cost of the 2-inch marble be \( x \) dollars. Then, the cost of the 1-inch marble, which is 30 cents less, would be \( x - 0.30 \) dollars.

Rochelle buys 25 1-inch marbles for a total of $10. Therefore, we can write the equation:

\[ 25(x - 0.30) = 10 \]

Now, we simplify the equation:

\[ 25x - 25 \times 0.30 = 10 \] \[ 25x - 7.50 = 10 \] \[ 25x = 10 + 7.50 \] \[ 25x = 17.50 \] \[ x = \frac{17.50}{25} = 0.70 \]

Thus, the cost of a 2-inch marble is \( \boxed{0.70} \) dollars.